This study proposed a procedure of using the energy method to evaluate the SSI-related damping effect when the soil–structure interaction (SSI) was considered in a bridge pier system, which can thus be deemed a soil–foundation–superstructure (SFS) inelastic system. Firstly, the SSI is implemented by adopting a discrete-time recursive filter approach as well as frequency-dependent foundation–soil impedance functions to solve for the external soil forces exerted onto the foundation. Then, by integrating such external soil forces into the motion equations of the SSI-based SFS system, the energy equations can be formulated during the ground motions. To demonstrate the proposed procedure, an implementation study involving a bridge pier was carried out, considering two earthquake recordings. The resultant energy quantities and SSI-related damping ratio shed light on how the aspects of earthquake characteristics affected the energy dissipation mechanism of the bridge pier SSI-based SFS system. This proposed procedure renders a promising solution for quantifying the soil role in the seismic energy dissipation of arbitrary single- and multiple-degree-of-freedom systems considering the SSI effect. The results obtained show that the SSI effect was suppressed when the SFS system underwent near-fault earthquakes, which illustrated that the stiffness and damping contribution from the soil was not pronounced. Furthermore, near-fault earthquakes with large incremental velocities may lead to a low SSI-related damping ratio (SSIDR).

This study aimed to investigate the effect of soil–structure interaction (SSI) on the inelastic displacement ratio of bridge structures subjected to near-fault pulse-like earthquake ground motions. SSI was modeled using a discrete-time recursive filter approach and frequency-dependent foundation–soil impedance functions. A total of 105 near-fault earthquake ground motion records were used for the analysis. The study also compared the soil–foundation–superstructure (SFS) system with a fixed-base system to explore the effects of spectral period normalization, strength reduction factor, earthquake magnitude, site-to-source distance, and peak ground velocity on the inelastic displacement ratio. The findings indicate that both the SFS and fixed-base systems have significant inelastic displacement demand under near-fault earthquakes, with values that can be 2–3 times higher than those predicted by ASCE-41-13, particularly in the short period range. Furthermore, as the structural period approaches the earthquake pulse period, the SFS system generally shows larger inelastic displacement ratios compared to the fixed-base system. The analytical results provide insight into the factors affecting the inelastic displacement ratio for near-fault pulse-like earthquakes.

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